Conditioning of Banach Space Valued Gaussian Random Variables: An Approximation Approach Based on Martingales

arXiv:2404.03453v1 Announce Type: cross
Abstract: In this paper we investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. These conditional distributions are again Gaussian and their means and covariances are determined by a general approximation scheme based upon a martingale idea. We then apply our general results to the case of Gaussian processes with continuous paths conditioned to partial observations of their paths.

abstract approximation arxiv cs.lg general math.pr math.st paper random space stat.th type variables